In any system of discrete masses and interconnecting elements, if the physical characteristics of the elements of the system are known, a mathematical relationship can be derived defining the motion and instantaneous position of each of the elements as a function of system excitation. An example of such a system is one represented by a plurality of masses interconnected by a plurality of springs. In such a spring-mass system, if the masses and the spring constants are known, then the movement of each element of the system can be defined in terms of the system excitation.
A turbine-generator system including plural turbine stages and a generator, with or without a rotating alternator (which may not be necessary if a static alternator is used) constitutes a complex system of many masses, some of which are large, as for example a generator or a turbine stage. On the other hand, many smaller masses such as couplings, gears and auxiliary systems are present. The many masses in a turbine-generator set are interconnected with varying shaft sections, all of which make up a composite shaft system. The respective shaft sections also have mass and inertia, but may be considered as having spring constants and are characterizable as springs (with the appropriate assumptions). Similarly, with appropriate assumptions limiting the number of masses to the principal masses of the system and by properly quantizing spring and mass parameters, it is possible to utilize the spring-mass system to analyze, identify and utilize oscillatory torque on the respective major shaft sections of the turbine-generator system. The application of the spring-mass method of analysis to a turbine-generator set is, however, in no sense of the word straightforward nor uncomplicated, but the principle is applicable if carefully applied.
Other complex rotating systems, with appropriate simplifying assumptions, may be similarly analyzed.
Any mechanical system has certain mechanical natural frequencies of oscillation at which the system may respond strongly to external stimuli. In a shaft-mass system, the number of mechanical natural frequencies of oscillation of the shafts is infinite, but if modeled by appropriate assumptions and characterizations so as to be treated as having a discrete number of masses and springs the number of natural frequencies of oscillation of the system is a function of the number of springs and masses, i.e., for a system of N masses, and N-1 interconnecting springs there will be N natural frequencies of oscillation. With large rotating shafts the oscillations of interest are torsional oscillations and, in the example of a turbine-generator system, considering the major components as discrete masses and the major shafts as discrete springs the predominant torsional natural frequencies of oscillation are in the sub-synchronous frequency range i.e., less than the generated frequency, e.g., 60 Hz, due to the relatively large masses of the system.
It has been found that in large turbine-generator systems, very small torsional oscillations in the shafts can cause stresses which may damage the shafts and in some instances result in shaft breakage and destruction of the system. Such damaging oscillations may have a peak amplitude as small as 0.01.degree.. It has also been found that the oscillations which can reach destructive proportions tend to have high components at the predominant torsional natural frequencies of oscillation. The oscillatory stress or torque at any point on any shaft in the system is the algebraic sum of all instantaneous stresses or torques of all frequencies at that point and time. Furthermore, the stresses in any shaft is proportional to the oscillatory torque on that shaft. Therefore, by determination of oscillating torque on each interconnecting shaft, it is possible to determine the stress in the shaft.
Accordingly, the present invention provides a method and apparatus for determination of instantaneous torque in each interconnecting section of a rotating shaft system by measurement of the amplitude of torsional oscillations at one or more points in the system.
Additionally, since the electrical output of the generator of a turbine-generator set contains component signals proportioned to the relative motion of the rotor with respect to the stator, this electrical signal may be analyzed exclusively or in addition to the measurements made upon the rotating system; likewise to determine the instantaneous torsional oscillation of the generator. Similarly, such electrical measurement may be practiced for the same purpose with respect to any dynamoelectric machine.
It is therefore an object of the present invention to provide a method and apparatus for determination of instantaneous torque in a rotating system.
It is a further object of the invention to provide a method and apparatus for determination of instantaneous torque in a rotating system by measurement of torsional oscillations at one or more points on the system.
It is yet another object of the invention to provide a method and apparatus for determination of instantaneous torque in each element of a plural element rotating system by measurement of instantaneous torsional oscillations at a chosen one of a plurality of available points in the system.
Another object of the invention is to provide a method and apparatus for analyzing the electrical output of a dynamoelectric machine to determine the instantaneous torsional oscillations thereof.
In carrying out the objects of this invention, in one form thereof, a turbine-generator viewed as a plurality of discrete masses and interconnecting shaft system together with torsional oscillation measurement arrangement therefor is shown. The torsional oscillation measurement arrangement in the described embodiment comprises apparatus for sensing instantaneous torsional oscillations in the system and developing a signal proportional to the amplitude of such oscillations and further comprises filters for extracting from the signal only those frequency components corresponding to the torsional natural frequencies of oscillation of the system. Such signals, whether representative of either electrical or shaft-mechanical measurements containing the component frequencies, can then be multiplied by appropriate constants in a plurality of electronic weighting networks to produce output signals proportional to oscillating torque. Each weighting network corresponds to a different shaft section and utilizes different multiplying constants which are dependent upon the characteristics of the total system. Recombining of the individual torque components caused by each individual frequency component results in signals proportional to total oscillating torque in each shaft section.